Observational constraints on the growth index parameters in $f(Q)$ gravity

TL;DR

This paper constrains the growth index parameters in $f(Q)$ gravity using recent cosmological data, finding slight deviations from the standard $ ext{ extLambda CDM}$ model and exploring various parametrizations of the growth index.

Contribution

It provides the first comprehensive analysis of growth index constraints in $f(Q)$ gravity with multiple parametrizations and datasets, highlighting deviations from $ ext{ extLambda CDM}$ expectations.

Findings

Growth index $ ext{ extGamma}_0$ constrained to 0.545 ± 0.096 in $ ext{ extLambda CDM}$

In $f(Q)$ gravity, $ ext{ extGamma}$ is slightly higher at 0.571^{+0.095}_{-0.110}

Time-varying $ ext{ extGamma}(z)$ spans from 0.596 to 0.62 across models

Abstract

In this study, we analyse constraints on the growth index of matter perturbations, $\gamma$, within the framework of $f(Q)$ gravity, using recent cosmological observations, at the background and the perturbation levels, including Pantheon$^{+}$, Cosmic Chronometer (CC), and Redshift Space Distortion (RSD) datasets. Our analysis focuses on quantifying the distortion parameter, which measures the deviation of the $f(Q)$ gravity model from the concordance $\Lambda$CDM cosmology at the background level. Specifically, we investigate two cases of the growth index parameter: a constant $\gamma$ and a time-varying $\gamma(z)$. We investigate various parametrizations of the growth index $\gamma$, expressed as $\gamma = \gamma_{0} +\gamma_{1} y(z)$, where the function $y(z)$ assumes different forms, including constant ($\Gamma_{0}$), Taylor expansion around $z = 0$ ($\Gamma_{1}$), Taylor expansion around the scale factor ($\Gamma_{2}$), and an exponential form ($\Gamma_{3}$). By employing the Akaike Information Criterion and Bayesian Information Criterion, we find that the combined Pantheon$^{+}$+ CC+ RSD datasets impose stringent constraints on the value of the growth index. For the $\Gamma_{0}$ model, our results indicate that within the concordance $\Lambda$CDM model, $\gamma$ is constrained to $0.545 \pm 0.096$, showing strong agreement with the theoretical expectation of $\gamma_{\Lambda} = \frac{6}{11}$. However, within the framework of $f(Q)$ gravity, we observe $\gamma = 0.571^{+0.095}_{-0.110}$, slightly exceeding the $\Lambda$CDM value by 4.66 $\%$. Furthermore, when considering a time-varying growth index, our analysis reveals that the range of $\gamma_{0}$ spans from $0.596$ to $0.62$ across the $\Gamma_{1-3}$ models.